Enhancing the Fault Ride-through Capability of a DFIG-WECS Using a High-Temperature Superconducting Coil

: With the increase in doubly fed induction generator-based wind energy conversion systems (DFIG-WECS) worldwide, improving the fault ride-through (FRT) capability of the entire system has been given much attention. Enhancement of the FRT capability of a DFIG-WECS is conventionally realized by employing a ﬂexible AC transmission system device with a proper control system. This paper presents a non-conventional method for the improvement of the FRT of DFIG-WECS, using a high-temperature superconducting coil interfaced with the DC-link of the rotor and stator side converters through a DC-chopper. A fractional-order proportional-integral (FOPI) controller is utilized to regulate the DC-chopper duty cycle in order to properly manage the power ﬂow between the DC-link and the coil. Two optimization techniques, Harmony Search and Grey Wolf Optimizer, are employed to determine the optimum size of the superconducting coil along with the optimum parameters of the FOPI controller. The effectiveness of the two proposed optimization techniques is highlighted through comparing their performance with the well-known particle swarm optimization technique.


Introduction
With the increased penetration of wind-based generation into power networks, major concerns such as poor power quality and a full or partial blackout may arise if a proper control system is not adopted [1][2][3]. The main restriction imposed on wind energy conversion systems (WECSs) is the voltage profile at the point of common coupling (PCC) with the main grid during faults and disturbance events. These voltage restrictions are presented in graphical plots showing the operating and tripping zones during fault events that the fault ride-through (FRT) capability of the WECS must comply with [4].
Doubly fed induction generators (DFIGs) are commonly used in many WECS installations due to their low initial cost, low converter rating and their active and reactive power controllability [5][6][7][8][9]. Despite these advantages, the most concerning downside of DFIGs is their susceptibility to faults at the grid side; in particular, voltage dips that call for the essential enhancement of the DFIG low voltage ride-through (LVRT) capability [8,9].
If not properly controlled, faults at the grid side increase the DFIG rotor mechanical speed, electromechanical torque and the rotor and stator currents. Under such conditions, the WECS must be disconnected to protect the converter switches, DFIG and wind turbines [8,9]. However, this may result in partial or full blackout, especially for large WECSs.

•
Enhancing the FRT capability of a WECS using a non-conventional method; hightemperature SC of solenoidal structure; • Introducing a new application for an FOPI controller in WECS; • Adopting two new optimization techniques; HS and GWO to determine the optimum design of the proposed high-temperature SC and the FOPI control parameters; • Presenting a comparison of HS and GWO techniques and the PSO to highlight the effectiveness of the employed methods.

System under Study and Proposed Controller
The studied DFIG-WECS is shown in Figure 1. The WECS comprised six DFIG generators, 1.5 MW each with rated voltage and frequency of 0.575 kV and 60 Hz. The stators of the DFIGs were connected to the electricity grid, represented as an infinite bus of constant voltage (120 kV) and frequency (60 Hz), through a three-phase step-up coupling transformer and a 30 km transmission line (TL). The rotors were connected to the low voltage side of the coupling transformer through two back-to-back converters: rotor side converter (RSC) and grid side converter (GSC), connected by a DC-capacitor link. Data of the system under study are listed in Tables A1 and A2 in the Appendix A.
effective than PSO and GA. On the other hand, GWO has been reported to be of better efficiency than the other seven optimization techniques [23].
From the above discussion, the main contribution of this paper can be summarized as below: • Enhancing the FRT capability of a WECS using a non-conventional method; hightemperature SC of solenoidal structure; • Introducing a new application for an FOPI controller in WECS; • Adopting two new optimization techniques; HS and GWO to determine the optimum design of the proposed high-temperature SC and the FOPI control parameters; • Presenting a comparison of HS and GWO techniques and the PSO to highlight the effectiveness of the employed methods.

System under Study and Proposed Controller
The studied DFIG-WECS is shown in Figure 1. The WECS comprised six DFIG generators, 1.5 MW each with rated voltage and frequency of 0.575 kV and 60 Hz. The stators of the DFIGs were connected to the electricity grid, represented as an infinite bus of constant voltage (120 kV) and frequency (60 Hz), through a three-phase step-up coupling transformer and a 30 km transmission line (TL). The rotors were connected to the low voltage side of the coupling transformer through two back-to-back converters: rotor side converter (RSC) and grid side converter (GSC), connected by a DC-capacitor link. Data of the system under study are listed in Tables A1 and A2 in the Appendix A.
The proposed high--temperature SC was interfaced to the DC-link of the GSC and RSC via a DC-chopper whose duty cycle was regulated to control the energy exchange between the coil and the system. Through a proper regulation to this energy exchange, the FRT capability of the WECS during fault incidents can be improved, as will be elaborated below. The proposed FOPI controller was used to enhance the FRT capability of the DFIG during fault events through regulating the duty cycle of the DC-chopper. During fault events and without the use of any controller, the DC-link voltage was expected to exhibit a significant oscillation that resulted in severe consequences to the entire system. By introducing optimally designed SC with a DC-chopper duty cycle regulated by an FOPI controller, a rapid regulation to the DC-link voltage was achieved. The proposed controller is as shown in Figure 2. In the proposed control system, the measured value of the DClink (VDClink) was compared to a reference voltage, VDClink_ref (1.15 kV in the studied system) to generate an error signal ΔVdc that was fed into the FOPI. The output of the FOPI controller was a regulated duty cycle deviation (ΔD) which was normalized between 0 and 1 and compared to a sawtooth signal to create a proper value for the DC-chopper duty cycle. The proposed high-temperature SC was interfaced to the DC-link of the GSC and RSC via a DC-chopper whose duty cycle was regulated to control the energy exchange between the coil and the system. Through a proper regulation to this energy exchange, the FRT capability of the WECS during fault incidents can be improved, as will be elaborated below.
The proposed FOPI controller was used to enhance the FRT capability of the DFIG during fault events through regulating the duty cycle of the DC-chopper. During fault events and without the use of any controller, the DC-link voltage was expected to exhibit a significant oscillation that resulted in severe consequences to the entire system. By introducing optimally designed SC with a DC-chopper duty cycle regulated by an FOPI controller, a rapid regulation to the DC-link voltage was achieved. The proposed controller is as shown in Figure 2. In the proposed control system, the measured value of the DC-link (V DClink ) was compared to a reference voltage, V DClink_ref (1.15 kV in the studied system) to generate an error signal ∆V dc that was fed into the FOPI. The output of the FOPI controller was a regulated duty cycle deviation (∆D) which was normalized between 0 and 1 and compared to a sawtooth signal to create a proper value for the DC-chopper duty cycle. The FOPI controller had three parameters, integration fractional order (λ), proportional constant (K p ) and integral constant (K i ) that are calculated below. The FOPI controller had three parameters, integration fractional order (λ), proportional constant (Kp) and integral constant (Ki) that are calculated below.

Evolutionary Computing Techniques
Three optimization techniques were presented to optimize the SC size and identify the FOPI control parameters. The main aim of these optimization techniques was to find the minimum SC size with minimum initial energy storage capacity along with the finetuning of the FOPI control parameters (Kp, Ki and λ) in order to improve the FRT capability of the entire system during disturbance and fault events.
In this regard, a multi-objective function J was formulated by considering the SC size (inductance, ), initial current in the SC ISC0 and the FOPI control parameters. The three optimization methods, HS, GWO and PSO, were used to minimize this objective function and thus identify the minimum SC rating with the least error in the DC-link voltage, ΔVdc. Hence, the proposed objective function comprised two terms: one was for the SC design and the other term was related to the error in the DC-link voltage as given by (1).
Subject to the below design constrains: 0.001 ≤ ≤ 10 , 1 ≤ ≤ 5 , and the FOPI three control parameters (Kp, Ki and λ) are all > 0. where is the initial current within the SC and and are arbitrary weighting factors that are selected as 0.5 and 1, respectively.
The objective function was non-linear and complex as it comprised five parameters, two related to the SC rating (ISCO, LSC) and three for the FOPI control parameters (Kp, Ki and λ). To solve such function, linear programming methods cannot provide an optimal global solution [8]. On the other hand, evolutionary computing techniques are the most suitable methods to solve such problems. In this paper, two modern optimization techniques (HS and GAW) were used to solve this problem. A comparison between these two methods and another well-known method, PSO, is presented to reveal the effectiveness of the two methods. The three methods are briefly elaborated below.
PSO is a well-known optimization method that has many applications in power system optimization [24][25][26][27]. PSO was employed in the SC design and optimal control of classical PI controller in [21].
HS is one of the modern evolutionary methods that can find many applications in power systems. HS was inspired by pitches grouping to attain leading harmony in musical organizations having to be amongst three playing dominion rules [28,29]: (i) Play any pitch concord as of the memory; (ii) Play any neighboring pitches of the pitch HS as of the memory; (iii) Play irregular pitch from the conceivable pitch.
In every variable selection from the HS algorithm imitation, the best (optimum) value searching procedure depends on the selection of a value and its adjacent ones from the

Evolutionary Computing Techniques
Three optimization techniques were presented to optimize the SC size and identify the FOPI control parameters. The main aim of these optimization techniques was to find the minimum SC size with minimum initial energy storage capacity along with the fine-tuning of the FOPI control parameters (K p , K i and λ) in order to improve the FRT capability of the entire system during disturbance and fault events.
In this regard, a multi-objective function J was formulated by considering the SC size (inductance, L sc ), initial current in the SC I SC0 and the FOPI control parameters. The three optimization methods, HS, GWO and PSO, were used to minimize this objective function and thus identify the minimum SC rating with the least error in the DC-link voltage, ∆V dc . Hence, the proposed objective function comprised two terms: one was for the SC design and the other term was related to the error in the DC-link voltage as given by (1).
Subject to the below design constrains: 0.001H ≤ L sc ≤ 10H, 1 kA ≤ I sco ≤ 5 kA, and the FOPI three control parameters (K p , K i and λ) are all > 0. where I sco is the initial current within the SC and W 1 and W 2 are arbitrary weighting factors that are selected as 0.5 and 1, respectively.
The objective function was non-linear and complex as it comprised five parameters, two related to the SC rating (I SCO , L SC ) and three for the FOPI control parameters (K p , K i and λ). To solve such function, linear programming methods cannot provide an optimal global solution [8]. On the other hand, evolutionary computing techniques are the most suitable methods to solve such problems. In this paper, two modern optimization techniques (HS and GAW) were used to solve this problem. A comparison between these two methods and another well-known method, PSO, is presented to reveal the effectiveness of the two methods. The three methods are briefly elaborated below.
PSO is a well-known optimization method that has many applications in power system optimization [24][25][26][27]. PSO was employed in the SC design and optimal control of classical PI controller in [21].
HS is one of the modern evolutionary methods that can find many applications in power systems. HS was inspired by pitches grouping to attain leading harmony in musical organizations having to be amongst three playing dominion rules [28,29]: (i) Play any pitch concord as of the memory; (ii) Play any neighboring pitches of the pitch HS as of the memory; (iii) Play irregular pitch from the conceivable pitch.
In every variable selection from the HS algorithm imitation, the best (optimum) value searching procedure depends on the selection of a value and its adjacent ones from the HS memory along with a random one from a possible range. Two main parameters are used to govern the HS algorithm; harmony memory considering rate (HMCR) and pitch adjusting Energies 2021, 14, 6319 5 of 18 rate (PAR). As shown in the flow chart of Figure 3, the first step in the HS is the initialization of the five unknown parameters of the objective function J by assuming random values within the limit of the designated ranges. Following the initializing process, the objective function is computed using (1). Harmony Memory (HM) matrix is then formulated as below.
The HM matrix comprises five columns, three for the FOPI control parameters and two for the SC inductance and initial current. Each row in the HM matrix is a progressed harmony vector primarily based on the HCMR and PAR parameters. The updated process on the current harmony is conducted using (3).
where x n i is the current harmony vector for all unknowns, x n+1 i is the updated harmony vector, rand is a random value in the range of (0, 1) and BW is an arbitrary distance bandwidth.
The updating process is repeated until a minimum possible value for the objective function is obtained or the maximum search number is reached.
GWO is another optimization technique that can be adopted in some power system applications [28,29]. This optimization technique is inspired by grey wolf social behavior which is based on leadership hierarchy structure. Grey wolves live in groups, with each group containing 5 to 12 wolves. In light of the chasing methodology of wolves, they can be arranged into four classifications. The first class is the alpha class (α), sometimes called dominant wolves. The wolves in this class have full authority to take decisions in all aspects of the group behavior, such as chasing time, chasing arrangement, resting time and place. They give strict decisions and instructions to the other wolves in the group.
The second class that follows the alpha is the beta (β). Wolves in this class help and provide advice to the alpha class in taking decisions, and replace the wolves in the alpha class in instances of absence or passing away. The third class is delta (δ), known as subordinate wolves. This class includes the elders, sentinels, hunters, scouts, and caretaker wolves.
Delta wolves look after the alpha and beta wolves and oversee the next level wolves. The omega (ω) class comprises the wolves in the most inferior position. These wolves must follow the instructions of all other classes. Omega wolves are not critical members but sometimes help others in facing internal issues. According to [22,29], the grey wolves' chasing technique is as follows: tracking, chasing, moving toward the prey, pursuing, surrounding, pestering the prey until a point when it stops moving, and finally attacking the prey.  The mathematical modelling of the GWO chasing technique is as below [24,30]: where → X p (t), → X(t) represent the position vector of the victim and grey wolf at any iteration step t, respectively, whereas → A and → C are two vectors that are calculated from: The vector → a is a linear decreasing vector from 2 to 0 over the iteration process and the two vectors In GWO, the initial best three solutions are saved and the other classes (including ω) are forced to update their positions to the best agent. The update is performed according to (8).
Then, the average of the best three positions as given by (9) is considered as the final best position.
The flow chart of the GWO process is shown in Figure 4. The flow chart of the GWO process is shown in Figure 4.

Results and Discussions
The convergence profiles of the objective function J using the three proposed optimization techniques over 150 iteration steps are shown in Figure 5. The results indicated that the GWO and HS provided better fitness than PSO with a superiority of GWO in converging to a minimum value of the objective function more rapidly than the other two techniques. The calculated SC size along with the FOPI control parameters using the three optimization methods are listed in Table

Results and Discussions
The convergence profiles of the objective function J using the three proposed optimization techniques over 150 iteration steps are shown in Figure 5. The results indicated that the GWO and HS provided better fitness than PSO with a superiority of GWO in converging to a minimum value of the objective function more rapidly than the other two techniques. The calculated SC size along with the FOPI control parameters using the three optimization methods are listed in Table 1. The table reveals that the least SC rating was obtained when employing GWO.
To test the effectiveness of the obtained results (minimum size of the SC along with the FOPI optimal parameters) using the three optimization techniques, two case studies were investigated: voltage swell and three-phase short circuit fault at the PCC of the system under study.

Case Study 1: Voltage Swell
In this case study, a severe voltage swell of 50% increment in the PCC voltage level, as shown in Figure 6, was assumed to take place at t = 2 s and last for 15 cycles. Without connecting the proposed SC and associated controller, the DC-link voltage shown in Figure 7 exhibited more than 13% increment above its nominal value with a maximum overshooting reaching 121% at t = 2 s. This increase in the DC-link voltage may destroy the capacitor that links the grid and rotor side converters of the DFIG or call for the disconnection of the wind turbines from the system. By using the proposed SC and the FOPI controller with the calculated parameters by the three optimization techniques, the voltage waveforms at the PCC and the DC-link were improved, as depicted in Figures 6  and 7, respectively. It can be observed that with the proposed SC, the overshooting in the DC-link voltage was significantly reduced, particularly when the parameters of the GWO were used, as illustrated in Figure 7. The generator's active and reactive powers during the voltage swell event are shown in Figure 8. Due to the voltage swell at the PCC, the generated active power exhibited significant oscillations during the swell event ( Figure  8a) and excess reactive power of about 1.4 pu was absorbed by the DFIGs as shown in Figure 8b. With the use of the proposed and optimized SC, the profiles of the active and reactive power were improved, particularly when the design parameters calculated by the GWO were employed.  To test the effectiveness of the obtained results (minimum size of the SC along with the FOPI optimal parameters) using the three optimization techniques, two case studies were investigated: voltage swell and three-phase short circuit fault at the PCC of the system under study.

Case Study 1: Voltage Swell
In this case study, a severe voltage swell of 50% increment in the PCC voltage level, as shown in Figure 6, was assumed to take place at t = 2 s and last for 15 cycles. Without connecting the proposed SC and associated controller, the DC-link voltage shown in Figure 7 exhibited more than 13% increment above its nominal value with a maximum overshooting reaching 121% at t = 2 s. This increase in the DC-link voltage may destroy the capacitor that links the grid and rotor side converters of the DFIG or call for the disconnection of the wind turbines from the system. By using the proposed SC and the FOPI controller with the calculated parameters by the three optimization techniques, the voltage waveforms at the PCC and the DC-link were improved, as depicted in Figures 6 and 7, respectively. It can be observed that with the proposed SC, the overshooting in the DClink voltage was significantly reduced, particularly when the parameters of the GWO were used, as illustrated in Figure 7. The generator's active and reactive powers during the voltage swell event are shown in Figure 8. Due to the voltage swell at the PCC, the generated active power exhibited significant oscillations during the swell event ( Figure 8a    Following the fluctuation in the generated active power, the rotor mechanical speed along with the electromagnetic torque also exhibited significant oscillations, as shown in Figure 9. These oscillations, without adding an SC to the system, may have an adverse impact on the mechanical parts of the generator and the turbine's blades. Mechanical oscillations were slightly improved when the proposed SC was connected.

Case Study 2: Three-Phase Short Circuit Fault
In this case study, a bolted three-phase short circuit fault was assumed to take place at the PCC at t = 2 s and last for 15 cycles, as shown in Figure 10.
The severe reduction in the voltage level violated most grid codes, such as the Spain and USA codes that are shown in Figure 10. This violation called for the disconnection of the wind turbines to prevent any possible damages. With the proposed control system, both active and reactive power at the PCC were regulated due to the energy exchange between the coil and the DC-link. As a result, the PCC voltage profile was enhanced and maintained within a safe margin in regard to the two mentioned codes, as shown in Figure 10. The results showed that the parameters calculated by the GWO and HS provided better performance than that calculated by the PSO. Following the fluctuation in the generated active power, the rotor mechanical speed along with the electromagnetic torque also exhibited significant oscillations, as shown in Figure 9. These oscillations, without adding an SC to the system, may have an adverse impact on the mechanical parts of the generator and the turbine's blades. Mechanical oscillations were slightly improved when the proposed SC was connected.
(a) The DC-link voltage encountered a significant increase that reached 157% of its nominal value if no control scheme was connected. With the connection of the SC and proposed controller, the DC-link voltage was almost kept at its nominal level, regardless of the short circuit fault at the PCC, as shown in Figure 11. Control sensitivity analysis through measuring the maximum overshooting, settling time, and steady-state error of the DC-link and the PCC voltages for this case study is given in Table 2. Results in this table revealed that the system performance when using the optimized parameters obtained from GWO was better than using the parameters obtained from PSO and HS methods. Following the fluctuation in the generated active power, the rotor mechanical speed along with the electromagnetic torque also exhibited significant oscillations, as shown in Figure 9. These oscillations, without adding an SC to the system, may have an adverse impact on the mechanical parts of the generator and the turbine's blades. Mechanical oscillations were slightly improved when the proposed SC was connected.

Case Study 2: Three-Phase Short Circuit Fault
In this case study, a bolted three-phase short circuit fault was assumed to take place at the PCC at t = 2 s and last for 15 cycles, as shown in Figure 10.
The severe reduction in the voltage level violated most grid codes, such as the Spain and USA codes that are shown in Figure 10. This violation called for the disconnection of the wind turbines to prevent any possible damages. With the proposed control system, both active and reactive power at the PCC were regulated due to the energy exchange between the coil and the DC-link.. As a result, the PCC voltage profile was enhanced and maintained within a safe margin in regard to the two mentioned codes, as shown in Figure  10. The results showed that the parameters calculated by the GWO and HS provided better performance than that calculated by the PSO.
The DC-link voltage encountered a significant increase that reached 157% of its nominal value if no control scheme was connected. With the connection of the SC and proposed controller, the DC-link voltage was almost kept at its nominal level, regardless of the short circuit fault at the PCC, as shown in Figure 11. Control sensitivity analysis through measuring the maximum overshooting, settling time, and steady-state error of the DC-link and the PCC voltages for this case study is given in Table 2. Results in this table revealed that the system performance when using the optimized parameters obtained from GWO was better than using the parameters obtained from PSO and HS methods.
The drop in the generator terminal voltage resulted in a significant decline in the generated active power and an increase in the reactive power to compensate the voltage    The drop in the generator terminal voltage resulted in a significant decline in the generated active power and an increase in the reactive power to compensate the voltage reduction as shown in Figure 12. With the connection of the SC, active power was injected by the coil, which raised the power at the PCC to about 0.57 pu when PSO was used, to 0.65 pu when HS was used, and to 0.85 pu when GWO was employed to optimize system parameters. The reactive power profile was also improved with the connection of the SC.
The three-phase fault increased the shaft speed ( Figure 13a) to 1.289 pu without the connection of the SC. The electromagnetic torque also increased with significant oscillations as shown in Figure 13b. With the proposed controller, the maximum shaft speed during the fault reached 1.27 pu, 1.265 pu and 1.26 pu by employing the control parameters obtained using the PSO, HS and GWO, respectively, and the profile of the electromagnetic torque was improved.   The three-phase fault increased the shaft speed ( Figure 13a) to 1.289 pu without the connection of the SC. The electromagnetic torque also increased with significant oscillations as shown in Figure 13b. With the proposed controller, the maximum shaft speed during the fault reached 1.27 pu, 1.265 pu and 1.26 pu by employing the control parameters obtained using the PSO, HS and GWO, respectively, and the profile of the electromagnetic torque was improved.
(a)  The three-phase fault increased the shaft speed ( Figure 13a) to 1.289 pu without the connection of the SC. The electromagnetic torque also increased with significant oscillations as shown in Figure 13b. With the proposed controller, the maximum shaft speed during the fault reached 1.27 pu, 1.265 pu and 1.26 pu by employing the control parameters obtained using the PSO, HS and GWO, respectively, and the profile of the electromagnetic torque was improved. The coil performance during this case study is illustrated in Figure 14. During normal operation, the voltage across the coil was maintained at zero level while the SC current was kept at its maximum positive level. This is because the duty cycle was adjusted by the controller to be 0.5 and based on the relation between the coil and DC-link voltages, , the voltage across the coil terminals became zero [8]. Under such The coil performance during this case study is illustrated in Figure 14. During normal operation, the voltage across the coil was maintained at zero level while the SC current was kept at its maximum positive level. This is because the duty cycle was adjusted by the controller to be 0.5 and based on the relation between the coil and DC-link voltages, V c = (1 − 2D)V DC−link , the voltage across the coil terminals became zero [8]. Under such normal conditions, there was no energy transfer between the coil and the system. Upon the occurrence of the fault at t = 2 s, the SC current, which is always unidirectional, dropped with a negative slope. This generated a voltage across the coil proportional with the rate of change of the current, i.e., with a negative polarity that facilitated the stored energy in the coil to be transferred to the system. It is worth noting that although the minimum SC size was obtained using GWO, this size provided the best performance because of the fine-tuning of the FOPI control parameters conducted by the GWO method.
The coil performance during this case study is illustrated in Figure 14. During normal operation, the voltage across the coil was maintained at zero level while the SC current was kept at its maximum positive level. This is because the duty cycle was adjusted by the controller to be 0.5 and based on the relation between the coil and DC-link voltages, = (1 − 2 ) − , the voltage across the coil terminals became zero [8]. Under such normal conditions, there was no energy transfer between the coil and the system. Upon the occurrence of the fault at t = 2 s, the SC current, which is always unidirectional, dropped with a negative slope. This generated a voltage across the coil proportional with the rate of change of the current, i.e., with a negative polarity that facilitated the stored energy in the coil to be transferred to the system. It is worth noting that although the

Cost Analysis
The high cost of low-temperature superconducting materials is dominated by the cryogenic system that uses liquid helium to maintain the conductor within a temperature less than 30 K. With the advancement of high-temperature-based superconductors, more affordable liquid nitrogen is employed by the cryogenic system to maintain the coil temperature within the range of 77 K to 160 K.
According to [31,32], the cost of a superconducting magnetic energy storage unit is estimated to be in the range of 7% to 25% of the overall cost of the wind energy conversion system it is connected to. It is worth noting that this cost includes the power transformer

Cost Analysis
The high cost of low-temperature superconducting materials is dominated by the cryogenic system that uses liquid helium to maintain the conductor within a temperature less than 30 K. With the advancement of high-temperature-based superconductors, Appendix A